"Let $V=M_{2\times2}(\mathbb{R})$ denote the vectors space of all $2\times2$ matrices with real number entries. Determine which of the following subsets are subspaces of $V$. If it is a subspace, find its dimension
F) All $2\times2$ matrices $A$ such that $A^T=−A$, where $A^T$ is the transpose of $A$.
I found that this was indeed a subspace, however, I'm having problem determining its dimension. I found the number of free variables to be one, so, the dimension should be one right? Also, what is the basis of this subspace so I can make sure that I'm on the right track.